Undersampling and the DTFT: Example #1

Sampling frequency 

[Graphics:../Images/index_gr_96.gif]

Continuous-time signal 

[Graphics:../Images/index_gr_97.gif]

[Graphics:../Images/index_gr_98.gif]

CTFT of infinite-length x(t) 

[Graphics:../Images/index_gr_99.gif]
[Graphics:../Images/index_gr_100.gif]
[Graphics:../Images/index_gr_101.gif]

[Graphics:../Images/index_gr_102.gif]

CTFT of finite-length x(t) 

[Graphics:../Images/index_gr_103.gif]
[Graphics:../Images/index_gr_104.gif]
[Graphics:../Images/index_gr_105.gif]

[Graphics:../Images/index_gr_106.gif]

Sampled waveform (finite-length) 

[Graphics:../Images/index_gr_107.gif]

[Graphics:../Images/index_gr_108.gif]

CTFT of infinite-length sampled signal 

[Graphics:../Images/index_gr_109.gif]
[Graphics:../Images/index_gr_110.gif]

[Graphics:../Images/index_gr_111.gif]

[Graphics:../Images/index_gr_112.gif]

[Graphics:../Images/index_gr_113.gif]

DTFT of finite-length sampled signal 

[Graphics:../Images/index_gr_114.gif]
[Graphics:../Images/index_gr_115.gif]

[Graphics:../Images/index_gr_116.gif]

Show all 

[Graphics:../Images/index_gr_117.gif]

[Graphics:../Images/index_gr_118.gif]

Converted by Mathematica      March 25, 2003